Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, m;
int grid[105][105], grid2[105][105];
int main() {
  int x;
  cin >> n >> m;
  int totalMove = 0;
  int minOfTheRow, minOfTheCol;
  vector<int> row(105, 0);
  vector<int> row2(105, 0);
  vector<int> col(105, 0);
  vector<int> col2(105, 0);
  for (int i = 1; i <= n; i++) {
    minOfTheRow = 1000;
    for (int j = 1; j <= m; j++) {
      cin >> grid[i][j];
      grid2[i][j] = grid[i][j];
      minOfTheRow = min(minOfTheRow, grid[i][j]);
    }
    if (minOfTheRow > 0) {
      row[i] = minOfTheRow;
      totalMove += minOfTheRow;
      for (int k = 1; k <= m; k++) {
        grid[i][k] -= minOfTheRow;
      }
    }
  }
  bool poss = true;
  for (int j = 1; j <= m; j++) {
    minOfTheCol = grid[1][j];
    for (int i = 1; i <= n; i++) {
      if (minOfTheCol != grid[i][j]) poss = false;
    }
    if (minOfTheCol > 0) {
      col[j] = minOfTheCol;
      totalMove += minOfTheCol;
      for (int k = 1; k <= n; k++) {
        grid[k][j] -= minOfTheCol;
      }
    }
  }
  int totalMove2 = 0;
  for (int j = 1; j <= m; j++) {
    minOfTheCol = 1000;
    for (int i = 1; i <= n; i++) {
      minOfTheCol = min(minOfTheCol, grid2[i][j]);
    }
    if (minOfTheCol > 0) {
      col2[j] = minOfTheCol;
      totalMove2 += minOfTheCol;
      for (int k = 1; k <= n; k++) {
        grid2[k][j] -= minOfTheCol;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    minOfTheRow = 1000;
    for (int j = 1; j <= m; j++) {
      cin >> grid2[i][j];
      minOfTheRow = min(minOfTheRow, grid2[i][j]);
    }
    if (minOfTheRow > 0) {
      row2[i] = minOfTheRow;
      totalMove2 += minOfTheRow;
      for (int k = 1; k <= m; k++) {
        grid2[i][k] -= minOfTheRow;
      }
    }
  }
  if (!poss) {
    cout << "-1" << endl;
    return 0;
  }
  cout << min(totalMove, totalMove2) << endl;
  if (totalMove2 < totalMove) {
    row = row2;
    col = col2;
  }
  for (int i = 1; i <= n; i++) {
    while (row[i] > 0) {
      row[i]--;
      cout << "row " << i << endl;
    }
  }
  for (int i = 1; i <= m; i++) {
    while (col[i] > 0) {
      col[i]--;
      cout << "col " << i << endl;
    }
  }
  return 0;
}